Perrin-Riou's integrality conjecture for the determinant of the big exponential map

Soient $V$ une représentation cristalline de $G_F$, $T$ un réseau de $V$, $M$ un réseau de $\mathbf{D}_{\mathrm{cris}}(V)$ satisfaisant la condition de comparaison donnée dans le texte, et $\omega$ la base induite de $\Delta_F(V)$. Soit $\Lambda$ l'algèbre d'Iwasawa et définissons

$$\delta_{\mathbf{Z}_p}(\Omega_V)=\prod_{j\geq 1-h}(\ell_{-j})^{-\dim_{\mathbf{Q}_p}\operatorname{Fil}^j\mathbf{D}_{\mathrm{cris}}(V)}\Omega_{V,h}[{\det}_{\Lambda}(\Lambda\otimes_{\mathbf{Z}_p}M)\otimes_{\Lambda}{\det}_{\Lambda}^{-1}H^1_{Iw}(F,T)\otimes_{\Lambda}{\det}_{\Lambda}H^2_{Iw}(F,T)].$$

Perrin-Riou's integrality conjecture. One has

$$\delta_{\mathbf{Z}_p}(\Omega_V)\in\Lambda^*.$$

The preceding text states that the corresponding rational-valued element lies in $\mathbf{Q}_p\otimes_{\mathbf{Z}_p}\Lambda$ and that Perrin-Riou conjectured its invertibility; it also says that Colmez proved the rational conjecture and the resulting product statement. The integral conjecture itself is not given a resolution status in the supplied text.